Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovsk...

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Main Authors: Yueying Liu, Ting Hou
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2018/3676083
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spelling doaj-7c0c474b83854ddf9de37cc7347d2f6e2020-11-25T00:17:35ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/36760833676083Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump SystemsYueying Liu0Ting Hou1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.http://dx.doi.org/10.1155/2018/3676083
collection DOAJ
language English
format Article
sources DOAJ
author Yueying Liu
Ting Hou
spellingShingle Yueying Liu
Ting Hou
Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
Discrete Dynamics in Nature and Society
author_facet Yueying Liu
Ting Hou
author_sort Yueying Liu
title Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
title_short Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
title_full Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
title_fullStr Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
title_full_unstemmed Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems
title_sort exponential stability and robust h∞ control for discrete-time time-delay infinite markov jump systems
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2018-01-01
description In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.
url http://dx.doi.org/10.1155/2018/3676083
work_keys_str_mv AT yueyingliu exponentialstabilityandrobusthcontrolfordiscretetimetimedelayinfinitemarkovjumpsystems
AT tinghou exponentialstabilityandrobusthcontrolfordiscretetimetimedelayinfinitemarkovjumpsystems
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